Using a mandolin or sharp knife, slice the zucchini length-wise into long and thin slices (about 1/4-inch thick). Then layer paper towels on your countertop. Spread the zucchini slices and sprinkle them with kosher salt.
Wait for 10-15 minutes to allow the excess liquid to be absorbed. Pat dry. (This step is very important to make before assembling your lasagna because it will help to draw out the moisture!)
Preheat oven to 375°.
In a skillet, heat olive oil over medium heat. Add mushrooms and cook 5-7 minutes until they are soft and golden.
Add garlic and sauté for 30 seconds, being careful not to burn.
Remove from the heat and set aside.
In a medium bowl, mix ricotta cheese, parmesan cheese, and an egg. Stir well. Using the same skillet you sautéed the mushrooms, spread some tomato sauce on the bottom.
Layer 6 or 7 zucchini slices to cover.
Place some of the ricotta cheese mixture and top with the mozzarella cheese.
Add again another layer of tomato sauce and then add the mushrooms.
Repeat the layers until all your ingredients are all used up.
Top with sauce and mozzarella.
Bake 40 minutes covered and 10 minutes uncovered.
Let stand about 15 minutes before serving.
Garnish with parsley.